The zero divisor problem for a class of torsion-free groups
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- by A. I. Lichtman PDF
- Proc. Amer. Math. Soc. 82 (1981), 188-190 Request permission
Abstract:
Let $G$ be a group, $N$ be a central torsion-free subgroup of $G$ and let $R$ be an arbitrary field. Then $R(G)$ contains no nilpotent elements provided that $R(G/N)$ contains no nilpotent elements. When $G$ is torsion-free the conditions of the theorem imply that $RG$ is a domain; this generalizes Passman’s theorem in [1].References
- D. S. Passman, Observations on group rings, Comm. Algebra 5 (1977), no. 11, 1119–1162. MR 457540, DOI 10.1080/00927877708822213 —, The algebraic structure of group rings, Pure and Appl. Math., Interscience, New York, 1977.
- Kenneth Hoffman and Ray Kunze, Linear algebra, 2nd ed., Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0276251
- Gilbert Baumslag, Wreath products and extensions, Math. Z. 81 (1963), 286–299. MR 151518, DOI 10.1007/BF01111576
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 188-190
- MSC: Primary 16A27
- DOI: https://doi.org/10.1090/S0002-9939-1981-0609648-0
- MathSciNet review: 609648